dynamic equilibria
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2021 ◽  
Author(s):  
Thomas Davidson

This paper introduces the concept of algorithmic opportunity structures to explore how the efficacy of online activism is contingent on the interaction between algorithms, activists, and audiences. In particular, I examine how far-right actors have gamed ranking and recommendation algorithms by producing content designed to generate high engagement rates. This tactic attracts algorithmic amplification, increasing their visibility and reach on social media. I consider the case of Britain First, a far-right, anti-Muslim movement that used Facebook to rapidly build the largest audience of any political organization in the United Kingdom. I use digital trace data, time series analysis, and topic modeling to study Britain First’s activity, recruitment, and support on Facebook. I identify dynamic equilibria indicative of algorithmically-mediated feedback loops, highlighting how variation in these processes is largely a function of user engagement. The content of the group’s posts and exogenous events, including elections and terrorist attacks, are also associated with short-term fluctuations in online mobilization. The results suggest that Britain First’s success is attributable to its exploitation of Facebook’s algorithms, demonstrating how technological assemblages designed and controlled by corporations can structure political competition and moderate opportunities for activism.


2021 ◽  
Vol 71 ◽  
pp. 215-222
Author(s):  
Laurel M. Pegram ◽  
Jake W. Anderson ◽  
Natalie G. Ahn

Author(s):  
Marcus Kaiser

We consider dynamic equilibria for flows over time under the fluid queuing model. In this model, queues on the links of a network take care of flow propagation. Flow enters the network at a single source and leaves at a single sink. In a dynamic equilibrium, every infinitesimally small flow particle reaches the sink as early as possible given the pattern of the rest of the flow. Although this model has been examined for many decades, progress has been relatively recent. In particular, the derivatives of dynamic equilibria have been characterized as thin flows with resetting, which allows for more structural results. Our two main results are based on the formulation of thin flows with resetting as a linear complementarity problem and its analysis. We present a constructive proof of existence for dynamic equilibria if the inflow rate is right-monotone. The complexity of computing thin flows with resetting, which occurs as a subproblem in this method, is still open. We settle it for the class of two-terminal, series-parallel networks by giving a recursive algorithm that solves the problem for all flow values simultaneously in polynomial time.


Author(s):  
Tobias Martin ◽  
Gang Wang ◽  
Hans Bihs

Abstract The significant difference in length scales between the flow around a moving fish net and the flow around each twine of the net prevents the resolution of the complete structure within a discrete fluid domain. In this paper, this issue is overcome by calculating the net and fluid dynamics separately and incorporate their interaction implicitly. The forces on the net are approximated using a screen force model, and the motion of the net is computed with a lumped mass method. Here, a linear system of equations is derived from the dynamic equilibria and kinematic relations. The net model is coupled to the CFD solver REEF3D which solves the incompressible Navier-Stokes equations using high-order finite differences in space and time. Several numerical calculations are provided, and the comparison of loads and velocity reduction with available measurements indicates the good performance of the proposed model.


2021 ◽  
Author(s):  
Jiaming Xiong ◽  
Caishan Liu

Abstract Finding the relative equilibria and analyzing their stabilities are of great significance to revealing the intrinsic properties of mechanical systems and developing effective controller. In this paper, we study the symmetry and relative equilibria of a bicycle system moving on a revolution surface. We note that the symmetry group of the bicycle is a three-dimensional Abelian Lie group, and the rolling condition of the two wheels produces four time-invariant first-order linear constraints to the bicycle system. Therefore, we can classify the bicycle dynamics as a general Voronets system whose Lagrangian and constraint distribution are kept invariant under the action of the symmetry group. Applying the Voronets equations to the bicycle dynamics, we obtain a seven-dimensional reduced dynamic system on the reduced constraint space. This system takes time-reversal and lateral symmetries, and has two kinds of relative equilibria: the static equilibria and the dynamic equilibria. Further theoretical analysis shows that both kinds of relative equilibria form one-parameter solution families, and their Jacobian matrices take some specific properties. We then show that a static equilibrium cannot be stable unless all the eigenvalues of the Jacobian matrix are located at the imaginary axis of the complex plane. The stability of the dynamic equilibria is studied by limiting the reduced dynamic system to an invariant manifold, which is established based on the conservation of energy of the system. We prove in a strict mathematical sense that the dynamic equilibria may be Lyapunov stable, but cannot be asymptotically stable. Finally, we employ symbolic computation to carry out numerical simulations in conjunction with the benchmark parameters of a Whipple bicycle. How the revolution surface affects the relative equilibria and their stabilities is then investigated through our numerical simulations.


2021 ◽  
Author(s):  
Roberto Cominetti ◽  
José Correa ◽  
Neil Olver

Steady State in Equilibrium for Flows over Time


2021 ◽  
Author(s):  
Klaus F. Steiner

AbstractBased on theoretical considerations and computer simulations, I show that living in groups brings advantages for cooperative traits through purely stochastic effects that result from the division of a population into groups. These advantages can be sufficient to compensate individual selection pressures that may be associated with the cooperative traits. In more complex agent-based simulation models, this effect combined with some migration between the groups leads to stable dynamic equilibria between cooperative and defective replicators in the population.


2021 ◽  
Author(s):  
Michael Liebthal ◽  
Manish Singh Kushwah ◽  
Philipp Kukura ◽  
Karl-Josef Dietz

AbstractSingle molecule mass photometry was used to study the dynamic equilibria of the ubiquitous and highly abundant 2-Cysteine peroxiredoxins (2-CysPRX). 2-CysPRXs adopt distinct functions in all cells dependent on their oligomeric conformation ranging from dimers to decamers and high molecular weight aggregates (HMW). The oligomeric state depends on the redox state of their catalytic cysteinyl residues. To which degree they interconvert, how the interconversion is regulated, and how the oligomerisation propensity is organism specific remains, however, poorly understood. The dynamics differs between wild-type and single point mutants affecting the oligomerization interfaces, with concomitant changes to function. Titrating concentration and redox state of Arabidopsis thaliana and human 2-CysPRXs revealed features conserved among all 2-CysPRX and clear differences concerning oligomer transitions, the occurrence of transition states and the formation of HMW which are associated with chaperone activity or storage. The results indicate functional differentiation of human 2-CysPRXs. Our results point to a diversified functionality of oligomerization for 2-CysPRXs and illustrate the power of mass photometry to non-invasively quantify oligomer distributions in a redox environment. This knowledge is important to fully address and model PRX function in cell redox signaling e.g., in photosynthesis, cardiovascular and neurological diseases or carcinogenesis.


2020 ◽  
Vol 7 (11) ◽  
pp. 201682
Author(s):  
Henri Kauhanen

People tend to align their use of language to the linguistic behaviour of their own ingroup and to simultaneously diverge from the language use of outgroups. This paper proposes to model this phenomenon of sociolinguistic identity maintenance as an evolutionary game in which individuals play the field and the dynamics are supplied by a multi-population extension of the replicator–mutator equation. Using linearization, the stabilities of all dynamic equilibria of the game in its fully symmetric two-population special case are found. The model is then applied to an empirical test case from adolescent sociolinguistic behaviour. It is found that the empirically attested population state corresponds to one of a number of stable equilibria of the game under an independently plausible value of a parameter controlling the rate of linguistic mutations. An asymmetric three-population extension of the game, explored with numerical solution methods, furthermore predicts to which specific equilibrium the system converges.


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